Management of a company that produces a medical device has carefully selected and screened 220 finished items (packaged, ready to ship). The team agrees that the sample contains 33 defective items, all for various visual defects on the package such as crooked labels, poor seal, errant marks on package, etc. The items are then given to an inspector for classification into “defective” and “non-defective” piles. The inspector ends up rejecting 9 non-defective items, and accepting 11 defective items. The
Management of a company that produces a medical device has carefully selected and screened 220 finished items (packaged, ready to ship). The team agrees that the sample contains 33 defective items, all for various visual defects on the package such as crooked labels, poor seal, errant marks on package, etc. The items are then given to an inspector for classification into “defective” and “non-defective” piles. The inspector ends up rejecting 9 non-defective items, and accepting 11 defective items. The inspector classifies the remaining items in the sample correctly. Find the following (answer as a probability, NOT a percentage. Use 3 decimal places. Notice that alpha = 9/187, Beta = 11/33, and p = 33/220.
P(inspector accepts the item and its actually non-defective) =
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